pfcoil_variables

N_PF_GROUPS_MAX = 10 module-attribute

maximum number of groups of PF coils

N_PF_COILS_IN_GROUP_MAX = 2 module-attribute

maximum number of PF coils in a given group

NPTSMX = 32 module-attribute

maximum number of points across the midplane of the plasma at which the field from the PF coils is fixed

NFIXMX = 64 module-attribute

maximum number of fixed current PF coils

NGC = N_PF_GROUPS_MAX * N_PF_COILS_IN_GROUP_MAX module-attribute

maximum total number of coils across all groups

NGC2 = NGC + 2 module-attribute

new variable to include 2 additional circuits: plasma and central solenoid

CREATE_DICTS_FROM_DATACLASS = PFCoilData module-attribute

PFCoilData dataclass

Source code in process/data_structure/pfcoil_variables.py

@dataclass
class PFCoilData:
    # PF coil module variables
    nef: int = 0

    nfxf: int = 0

    ricpf: float = 0.0

    ssq0: float = 0.0

    stress_z_cs_self_peak_midplane: float = 0.0
    """Peak axial stress (z) in central solenoid at midplane due to its own field (when at peak current) (Pa)"""

    stress_z_cs_self_midplane_profile: list[float] = field(
        default_factory=lambda: np.zeros(6)
    )
    """Axial stress (z) in central solenoid at midplane due to its own field at each time point (Pa)"""

    sig_hoop: float = 0.0

    forc_z_cs_self_peak_midplane: float = 0.0
    """Axial force (z) on central solenoid at midplane due to its own field (when at peak current) (N)"""

    r_pf_cs_current_filaments: list[float] = field(
        default_factory=lambda: np.zeros(NFIXMX)
    )
    """array of radial positions of current filaments in central solenoid"""

    z_pf_cs_current_filaments: list[float] = field(
        default_factory=lambda: np.zeros(NFIXMX)
    )
    """array of vertical positions of current filaments in central solenoid"""

    c_pf_cs_current_filaments: list[float] = field(
        default_factory=lambda: np.zeros(NFIXMX)
    )
    """array of current in filaments in central solenoid"""

    xind: list[float] = field(default_factory=lambda: np.zeros(NFIXMX))

    r_pf_coil_middle_group_array: list[float] = field(
        default_factory=lambda: np.zeros((N_PF_GROUPS_MAX, N_PF_COILS_IN_GROUP_MAX))
    )
    """2D array of PF coil middle radii, indexed by group and coil in group"""

    z_pf_coil_middle_group_array: list[float] = field(
        default_factory=lambda: np.zeros((N_PF_GROUPS_MAX, N_PF_COILS_IN_GROUP_MAX))
    )
    """2D array of PF coil middle heights, indexed by group and coil in group"""

    ccls: list[float] = field(default_factory=lambda: np.zeros(N_PF_GROUPS_MAX))

    ccl0: list[float] = field(default_factory=lambda: np.zeros(N_PF_GROUPS_MAX))

    bpf2: list[float] = field(default_factory=lambda: np.zeros(NGC2))

    vsdum: list[float] = field(default_factory=lambda: np.zeros((NGC2, 3)))

    first_call: bool = True

    cslimit: bool = False

    # PF coil variables

    alfapf: float = 5e-10
    """smoothing parameter used in PF coil current calculation at the beginning of pulse (BoP)"""

    alstroh: float = 4.0e8
    """allowable hoop stress in Central Solenoid structural material (Pa)"""

    i_cs_stress: int = 1
    """Switch for CS stress calculation:
    - =0 Hoop stress only
    - =1 Hoop + Axial stress
    """

    a_cs_poloidal: float = 0.0
    """Central solenoid vertical cross-sectional area (m2)"""

    a_cs_turn: float = 0.0
    """Central solenoid (OH) trun cross-sectional area (m2)"""

    awpoh: float = 0.0
    """central solenoid conductor+void area with area of steel subtracted (m2)"""

    b_cs_peak_flat_top_end: float = 0.0
    """maximum field in central solenoid at end of flat-top (EoF) (T)"""

    b_cs_peak_pulse_start: float = 0.0
    """maximum field in central solenoid at beginning of pulse (T)"""

    b_pf_coil_peak: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """peak field at coil i (T)"""

    ccl0_ma: list[float] = field(default_factory=lambda: np.zeros(N_PF_GROUPS_MAX))
    """PF group current array, flux-swing cancellation current (MA)
    Input if i_pf_current=0, computed otherwise
    """

    ccls_ma: list[float] = field(default_factory=lambda: np.zeros(N_PF_GROUPS_MAX))
    """PF group current array, equilibrium current (MA)
    Input if i_pf_current=0, computed otherwise
    """

    j_cs_pulse_start: float = 0.0
    """Central solenoid overall current density at beginning of pulse (A/m2)"""

    j_cs_flat_top_end: float = 1.85e7
    """Central solenoid overall current density at end of flat-top (A/m2) (`iteration variable 37`) (`sweep variable 62`)"""

    c_pf_coil_turn: list[float] = field(default_factory=lambda: np.zeros((NGC2, 6)))
    """current per turn in coil i at time j (A)"""

    c_pf_coil_turn_peak_input: list[float] = field(
        default_factory=lambda: np.full(NGC2, 4.0e4)
    )
    """peak current per turn input for PF coil i (A)"""

    c_pf_cs_coil_pulse_start_ma: list[float] = field(
        default_factory=lambda: np.zeros(NGC2)
    )
    """PF coil current array, at beginning of pulse (MA)
    Indexed by coil number, not group number
    """

    c_pf_cs_coil_flat_top_ma: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """PF coil current array, at flat top (MA)
    Indexed by coil number, not group number
    """

    c_pf_cs_coil_pulse_end_ma: list[float] = field(
        default_factory=lambda: np.zeros(NGC2)
    )
    """PF coil current array, at end of pulse (MA)
    Indexed by coil number, not group number
    """

    etapsu: float = 0.9
    """Efficiency of transfer of PF stored energy into or out of storage."""

    f_j_cs_start_end_flat_top: float = 0.0
    """ratio of central solenoid overall current density at beginning of flat-top / end of flat-top"""

    f_j_cs_start_pulse_end_flat_top: float = 0.9
    """ratio of central solenoid overall current density at beginning of pulse / end of flat-top
    (`iteration variable 41`)
    """

    fcuohsu: float = 0.7
    """copper fraction of strand in central solenoid"""

    fcupfsu: float = 0.69
    """copper fraction of cable conductor (PF coils)"""

    i_pf_location: list[int] = field(
        default_factory=lambda: np.array([2, 2, 3, 0, 0, 0, 0, 0, 0, 0])
    )
    """Switch for location of PF coil group i:
    - =1 PF coil on top of central solenoid (flux ramp only)
    - =2 PF coil on top of TF coil (flux ramp only)
    - =3 PF coil outside of TF coil (equilibrium coil)
    - =4 PF coil, general location (equilibrium coil)
    """

    i_pf_conductor: int = 0
    """switch for PF & CS coil conductor type:
    - =0 superconducting PF coils
    - =1 resistive PF coils
    """

    itr_sum: float = 0.0
    """total sum of I x turns x radius for all PF coils and CS (Am)"""

    i_cs_superconductor: int = 1
    """switch for superconductor material in central solenoid:
    - =1 ITER Nb3Sn critical surface model with standard
    ITER parameters
    - =2 Bi-2212 high temperature superconductor (range of
    validity T < 20K, adjusted field b < 104 T, B > 6 T)
    - =3 NbTi
    - =4 ITER Nb3Sn model with user-specified parameters
    - =5 WST Nb3Sn parameterisation
    - =6 REBCO HTS tape in CroCo strand
    - =7 Durham Ginzburg-Landau critical surface model for Nb-Ti
    - =8 Durham Ginzburg-Landau critical surface model for REBCO
    - =9 Hazelton experimental data + Zhai conceptual model for REBCO
    """

    i_pf_superconductor: int = 1
    """switch for superconductor material in PF coils:
    - =1 ITER Nb3Sn critical surface model with standard
    ITER parameters
    - =2 Bi-2212 high temperature superconductor (range of
    validity T < 20K, adjusted field b < 104 T, B > 6 T)
    - =3 NbTi
    - =4 ITER Nb3Sn model with user-specified parameters
    - =5 WST Nb3Sn parameterisation
    - =6 REBCO HTS tape in CroCo strand
    - =7 Durham Ginzburg-Landau critical surface model for Nb-Ti
    - =8 Durham Ginzburg-Landau critical surface model for REBCO
    - =9 Hazelton experimental data + Zhai conceptual model for REBCO
    """

    j_crit_str_cs: float = 0.0
    """superconductor strand critical current density under operating
    conditions in central solenoid (A/m2). Necessary for the cost calculation in $/kA m
    """

    j_crit_str_pf: float = 0.0
    """superconductor strand critical current density under operating
    conditions in PF coils (A/m2). Necessary for the cost calculation in $/kA m
    """

    i_pf_current: int = 1
    """Switch for controlling the current of the PF coils:
    - =0 Input via the variables c_pf_cs_coil_pulse_start_ma, c_pf_cs_coil_flat_top_ma, c_pf_cs_coil_pulse_end_ma
    - =1 SVD targets zero field across midplane (flux swing
    coils) and the correct vertical field at the plasma
    center (equilibrium coils)
    """

    i_r_pf_outside_tf_placement: int = 0
    """Switch for the placement of Location 3 (outboard) PF coils
    - =0 (Default) Outboard PF coils follow TF shape
    in an ellipsoidal winding surface
    - =1 Outboard PF coils all have same radius, cylindrical
    winding surface
    """

    j_cs_conductor_critical_pulse_start: float = 0.0
    """central solenoid superconductor critical current density (A/m2) at beginning-of-pulse"""

    j_cs_conductor_critical_flat_top_end: float = 0.0
    """central solenoid superconductor critical current density (A/m2) at end-of-flattop"""

    jcableoh_bop: float = 0.0
    """central solenoid cable critical current density (A/m2) at beginning-of-pulse"""

    jcableoh_eof: float = 0.0
    """central solenoid cable critical current density (A/m2) at end-of-flattop"""

    n_pf_cs_plasma_circuits: int = 0
    """number of PF circuits (including central solenoid and plasma)"""

    n_pf_coils_in_group: list[int] = field(
        default_factory=lambda: np.array([1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0])
    )
    """number of PF coils in group j"""

    n_cs_current_filaments: int = 7
    """number of filaments the top and bottom of the central solenoid should be broken
    into during scaling (5 - 10 is good)
    """

    n_pf_coil_groups: int = 3
    """number of groups of PF coils. Symmetric coil pairs should all be in the same group"""

    n_cs_pf_coils: int = 0
    """number of PF coils (excluding the central solenoid) + 1"""

    f_z_cs_tf_internal: float = 0.71
    """Central solenoid height / TF coil internal height"""

    f_a_cs_turn_steel: float = 0.5
    """Fraction of CS turn poloidal area that is steel (`iteration variable 122`)"""

    pf_current_safety_factor: float = 1.0
    """Ratio of permissible PF coil conductor current density to critical conductor
    current density based on short-sample DC measurements
    """

    pfcaseth: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """steel case thickness for PF coil i (m)"""

    rho_pf_coil: float = 2.5e-8
    """PF coil resistivity (if i_pf_conductor=1) (Ohm-m)"""

    rhopfbus: float = 3.93e-8
    """Resistivity of CS and PF coil bus bars (irrespective of
    whether the coils themselves are superconducting or resistive) (Ohm-m)
    """

    m_pf_coil_max: float = 0.0
    """mass of heaviest PF coil (tonnes)"""

    r_pf_coil_outer_max: float = 0.0
    """radius of largest PF coil (m)"""

    p_pf_electric_supplies_mw: float = 0.0
    """Total mean wall plug power dissipated in PFC and CS power supplies (MW) (issue #713)"""

    p_cs_resistive_flat_top: float = 0.0
    """central solenoid resistive power during flattop (W)"""

    p_pf_coil_resistive_total_flat_top: float = 0.0
    """total PF coil resistive losses during flattop (W)"""

    r_pf_coil_inner: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """inner radius of coil i (m)"""

    r_pf_coil_outer: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """outer radius of coil i (m)"""

    c_pf_cs_coils_peak_ma: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """peak current in coil i (MA-turns)"""

    j_pf_coil_wp_peak: list[float] = field(default_factory=lambda: np.full(NGC2, 3.0e7))
    """average winding pack current density of PF coil i (A/m2) at time of peak
    current in that coil (calculated for `i_pf_location=1` coils)
    """

    j_cs_critical_flat_top_end: float = 0.0
    """allowable central solenoid current density at end of flat-top (A/m2)"""

    j_cs_critical_pulse_start: float = 0.0
    """allowable central solenoid current density at beginning of pulse (A/m2)"""

    j_pf_wp_critical: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """allowable winding pack current density of PF coil i (A/m2)"""

    r_cs_middle: float = 0.0
    """radius to the centre of the central solenoid (m)"""

    dz_cs_full: float = 0.0
    """Full height of the central solenoid (m)"""

    dr_pf_tf_outboard_out_offset: float = 1.5
    """radial distance (m) from outboard TF coil leg to centre of `i_pf_location=3` PF coils"""

    r_pf_coil_middle: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """radius of PF coil i (m)"""

    dr_pf_cs_middle_offset: float = 0.0
    """offset (m) of radial position of `i_pf_location=1` PF coils from being directly above
    the central solenoid
    """

    rpf2: float = -1.63
    """offset (m) of radial position of `i_pf_location=2` PF coils from being at
    rmajor (offset = rpf2*triang*rminor)
    """

    rref: list[float] = field(default_factory=lambda: np.full(N_PF_GROUPS_MAX, 7.0))
    """PF coil radial positioning adjuster:
    - for groups j with i_pf_location(j) = 1; rref(j) is ignored
    - for groups j with i_pf_location(j) = 2; rref(j) is ignored
    - for groups j with i_pf_location(j) = 3; rref(j) is ignored
    - for groups j with i_pf_location(j) = 4; rref(j) is radius of
    the coil in units of minor radii from the major radius
    (r = rmajor + rref*rminor)
    """

    s_shear_cs_peak: float = 0.0
    """Maximum shear stress (Tresca criterion) coils/central solenoid [MPa]"""

    sigpfcalw: float = 500.0
    """maximum permissible tensile stress (MPa) in steel coil cases for superconducting
    PF coils (`i_pf_conductor=0`)
    """

    sigpfcf: float = 1.0
    """fraction of JxB hoop force supported by steel case for superconducting PF coils (`i_pf_conductor=0`)"""

    ind_pf_cs_plasma_mutual: list[float] = field(
        default_factory=lambda: np.zeros((NGC2, NGC2))
    )
    """mutual inductance matrix (H)"""

    temp_cs_superconductor_margin: float = 0.0
    """Central solenoid temperature margin (K)"""

    n_pf_coil_turns: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """number of turns in PF coil i"""

    f_a_pf_coil_void: list[float] = field(default_factory=lambda: np.full(NGC2, 0.3))
    """winding pack void fraction of PF coil i for coolant"""

    f_a_cs_void: float = 0.3
    """void fraction of central solenoid conductor for coolant"""

    vs_cs_pf_total_burn: float = 0.0
    """total flux swing available for burn (Wb)"""

    vs_pf_coils_total_burn: float = 0.0
    """flux swing from PF coils for burn (Wb)"""

    vs_pf_coils_total_ramp: float = 0.0
    """flux swing from PF coils for startup (Wb)"""

    vs_pf_coils_total_pulse: float = 0.0
    """total flux swing from PF coils (Wb)"""

    vs_cs_total_pulse: float = 0.0
    """total flux swing from the central solenoid (Wb)"""

    vs_cs_burn: float = 0.0
    """central solenoid flux swing for burn (Wb)"""

    vs_cs_ramp: float = 0.0
    """central solenoid flux swing for startup (Wb)"""

    vs_cs_pf_total_ramp: float = 0.0
    """total flux swing for startup (`constraint eqn 51` to enforce vs_cs_pf_total_ramp=vs_plasma_res_ramp+vs_plasma_ind_ramp) (Wb)"""

    vs_cs_pf_total_pulse: float = 0.0
    """total flux swing for pulse (Wb)"""

    f_c_pf_cs_peak_time_array: list[float] = field(
        default_factory=lambda: np.zeros((NGC2, 6))
    )
    """PF, CS coil current relative to peak current at time points 1 to 6"""

    m_pf_coil_conductor_total: float = 0.0
    """total mass of the PF coil conductor (kg)"""

    m_pf_coil_structure_total: float = 0.0
    """total mass of the PF coil structure (kg)"""

    m_pf_coil_conductor: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """conductor mass for PF coil i (kg)"""

    m_pf_coil_structure: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """structure mass for PF coil i (kg)"""

    z_pf_coil_upper: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """upper point of PF coil i (m)"""

    z_pf_coil_lower: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """lower point of PF coil i (m)"""

    z_pf_coil_middle: list[float] = field(default_factory=lambda: np.zeros(NGC2))
    """z (height) location of PF coil i (m)"""

    zref: list[float] = field(
        default_factory=lambda: np.array([
            3.6,
            1.2,
            2.5,
            1.0,
            1.0,
            1.0,
            1.0,
            1.0,
            1.0,
            1.0,
        ])
    )
    """PF coil vertical positioning adjuster:
    - for groups j with i_pf_location(j) = 1; zref(j) is ignored
    - for groups j with i_pf_location(j) = 2 AND itart=1 (only);
    zref(j) is distance of centre of PF coil from inside
    edge of TF coil (remember that PF coils for STs lie
    within the TF coil)
    - for groups j with i_pf_location(j) = 3; zref(j) = ratio of
    height of coil group j to plasma minor radius</UL>
    - for groups j with i_pf_location(j) = 4; zref(j) = ratio of
    height of coil group j to plasma minor radius</UL>
    """

    b_cs_limit_max: float = 13.0
    """Central solenoid max field limit [T]"""

    f_dr_dz_cs_turn: float = 70.0 / 22.0
    """Ratio of CS coil turn conduit length to depth"""

    dr_cs_turn: float = 0.0
    """Length of CS of CS coil turn conduit"""

    dr_cs_full: float = 0.0
    """Full radial thickness of the central solenoid (m)"""

    dz_cs_turn: float = 0.0
    """Depth/width of CS of CS coil turn conduit"""

    radius_cs_turn_corners: float = 3.0e-3
    """Radius of curvature of CS coil turn corners (m)"""

    radius_cs_turn_cable_space: float = 0.0
    """Length of CS of CS coil turn conduit length"""

nef = 0 class-attribute instance-attribute

nfxf = 0 class-attribute instance-attribute

ricpf = 0.0 class-attribute instance-attribute

ssq0 = 0.0 class-attribute instance-attribute

stress_z_cs_self_peak_midplane = 0.0 class-attribute instance-attribute

Peak axial stress (z) in central solenoid at midplane due to its own field (when at peak current) (Pa)

stress_z_cs_self_midplane_profile = field(default_factory=(lambda: np.zeros(6))) class-attribute instance-attribute

Axial stress (z) in central solenoid at midplane due to its own field at each time point (Pa)

sig_hoop = 0.0 class-attribute instance-attribute

forc_z_cs_self_peak_midplane = 0.0 class-attribute instance-attribute

Axial force (z) on central solenoid at midplane due to its own field (when at peak current) (N)

r_pf_cs_current_filaments = field(default_factory=(lambda: np.zeros(NFIXMX))) class-attribute instance-attribute

array of radial positions of current filaments in central solenoid

z_pf_cs_current_filaments = field(default_factory=(lambda: np.zeros(NFIXMX))) class-attribute instance-attribute

array of vertical positions of current filaments in central solenoid

c_pf_cs_current_filaments = field(default_factory=(lambda: np.zeros(NFIXMX))) class-attribute instance-attribute

array of current in filaments in central solenoid

xind = field(default_factory=(lambda: np.zeros(NFIXMX))) class-attribute instance-attribute

r_pf_coil_middle_group_array = field(default_factory=(lambda: np.zeros((N_PF_GROUPS_MAX, N_PF_COILS_IN_GROUP_MAX)))) class-attribute instance-attribute

2D array of PF coil middle radii, indexed by group and coil in group

z_pf_coil_middle_group_array = field(default_factory=(lambda: np.zeros((N_PF_GROUPS_MAX, N_PF_COILS_IN_GROUP_MAX)))) class-attribute instance-attribute

2D array of PF coil middle heights, indexed by group and coil in group

ccls = field(default_factory=(lambda: np.zeros(N_PF_GROUPS_MAX))) class-attribute instance-attribute

ccl0 = field(default_factory=(lambda: np.zeros(N_PF_GROUPS_MAX))) class-attribute instance-attribute

bpf2 = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

vsdum = field(default_factory=(lambda: np.zeros((NGC2, 3)))) class-attribute instance-attribute

first_call = True class-attribute instance-attribute

cslimit = False class-attribute instance-attribute

alfapf = 5e-10 class-attribute instance-attribute

smoothing parameter used in PF coil current calculation at the beginning of pulse (BoP)

alstroh = 400000000.0 class-attribute instance-attribute

allowable hoop stress in Central Solenoid structural material (Pa)

i_cs_stress = 1 class-attribute instance-attribute

Switch for CS stress calculation: - =0 Hoop stress only - =1 Hoop + Axial stress

a_cs_poloidal = 0.0 class-attribute instance-attribute

Central solenoid vertical cross-sectional area (m2)

a_cs_turn = 0.0 class-attribute instance-attribute

Central solenoid (OH) trun cross-sectional area (m2)

awpoh = 0.0 class-attribute instance-attribute

central solenoid conductor+void area with area of steel subtracted (m2)

b_cs_peak_flat_top_end = 0.0 class-attribute instance-attribute

maximum field in central solenoid at end of flat-top (EoF) (T)

b_cs_peak_pulse_start = 0.0 class-attribute instance-attribute

maximum field in central solenoid at beginning of pulse (T)

b_pf_coil_peak = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

peak field at coil i (T)

ccl0_ma = field(default_factory=(lambda: np.zeros(N_PF_GROUPS_MAX))) class-attribute instance-attribute

PF group current array, flux-swing cancellation current (MA) Input if i_pf_current=0, computed otherwise

ccls_ma = field(default_factory=(lambda: np.zeros(N_PF_GROUPS_MAX))) class-attribute instance-attribute

PF group current array, equilibrium current (MA) Input if i_pf_current=0, computed otherwise

j_cs_pulse_start = 0.0 class-attribute instance-attribute

Central solenoid overall current density at beginning of pulse (A/m2)

j_cs_flat_top_end = 18500000.0 class-attribute instance-attribute

Central solenoid overall current density at end of flat-top (A/m2) (iteration variable 37) (sweep variable 62)

c_pf_coil_turn = field(default_factory=(lambda: np.zeros((NGC2, 6)))) class-attribute instance-attribute

current per turn in coil i at time j (A)

c_pf_coil_turn_peak_input = field(default_factory=(lambda: np.full(NGC2, 40000.0))) class-attribute instance-attribute

peak current per turn input for PF coil i (A)

c_pf_cs_coil_pulse_start_ma = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

PF coil current array, at beginning of pulse (MA) Indexed by coil number, not group number

c_pf_cs_coil_flat_top_ma = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

PF coil current array, at flat top (MA) Indexed by coil number, not group number

c_pf_cs_coil_pulse_end_ma = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

PF coil current array, at end of pulse (MA) Indexed by coil number, not group number

etapsu = 0.9 class-attribute instance-attribute

Efficiency of transfer of PF stored energy into or out of storage.

f_j_cs_start_end_flat_top = 0.0 class-attribute instance-attribute

ratio of central solenoid overall current density at beginning of flat-top / end of flat-top

f_j_cs_start_pulse_end_flat_top = 0.9 class-attribute instance-attribute

ratio of central solenoid overall current density at beginning of pulse / end of flat-top (iteration variable 41)

fcuohsu = 0.7 class-attribute instance-attribute

copper fraction of strand in central solenoid

fcupfsu = 0.69 class-attribute instance-attribute

copper fraction of cable conductor (PF coils)

i_pf_location = field(default_factory=(lambda: np.array([2, 2, 3, 0, 0, 0, 0, 0, 0, 0]))) class-attribute instance-attribute

Switch for location of PF coil group i: - =1 PF coil on top of central solenoid (flux ramp only) - =2 PF coil on top of TF coil (flux ramp only) - =3 PF coil outside of TF coil (equilibrium coil) - =4 PF coil, general location (equilibrium coil)

i_pf_conductor = 0 class-attribute instance-attribute

switch for PF & CS coil conductor type: - =0 superconducting PF coils - =1 resistive PF coils

itr_sum = 0.0 class-attribute instance-attribute

total sum of I x turns x radius for all PF coils and CS (Am)

i_cs_superconductor = 1 class-attribute instance-attribute

switch for superconductor material in central solenoid: - =1 ITER Nb3Sn critical surface model with standard ITER parameters - =2 Bi-2212 high temperature superconductor (range of validity T < 20K, adjusted field b < 104 T, B > 6 T) - =3 NbTi - =4 ITER Nb3Sn model with user-specified parameters - =5 WST Nb3Sn parameterisation - =6 REBCO HTS tape in CroCo strand - =7 Durham Ginzburg-Landau critical surface model for Nb-Ti - =8 Durham Ginzburg-Landau critical surface model for REBCO - =9 Hazelton experimental data + Zhai conceptual model for REBCO

i_pf_superconductor = 1 class-attribute instance-attribute

switch for superconductor material in PF coils: - =1 ITER Nb3Sn critical surface model with standard ITER parameters - =2 Bi-2212 high temperature superconductor (range of validity T < 20K, adjusted field b < 104 T, B > 6 T) - =3 NbTi - =4 ITER Nb3Sn model with user-specified parameters - =5 WST Nb3Sn parameterisation - =6 REBCO HTS tape in CroCo strand - =7 Durham Ginzburg-Landau critical surface model for Nb-Ti - =8 Durham Ginzburg-Landau critical surface model for REBCO - =9 Hazelton experimental data + Zhai conceptual model for REBCO

j_crit_str_cs = 0.0 class-attribute instance-attribute

superconductor strand critical current density under operating conditions in central solenoid (A/m2). Necessary for the cost calculation in $/kA m

j_crit_str_pf = 0.0 class-attribute instance-attribute

superconductor strand critical current density under operating conditions in PF coils (A/m2). Necessary for the cost calculation in $/kA m

i_pf_current = 1 class-attribute instance-attribute

Switch for controlling the current of the PF coils: - =0 Input via the variables c_pf_cs_coil_pulse_start_ma, c_pf_cs_coil_flat_top_ma, c_pf_cs_coil_pulse_end_ma - =1 SVD targets zero field across midplane (flux swing coils) and the correct vertical field at the plasma center (equilibrium coils)

i_r_pf_outside_tf_placement = 0 class-attribute instance-attribute

Switch for the placement of Location 3 (outboard) PF coils - =0 (Default) Outboard PF coils follow TF shape in an ellipsoidal winding surface - =1 Outboard PF coils all have same radius, cylindrical winding surface

j_cs_conductor_critical_pulse_start = 0.0 class-attribute instance-attribute

central solenoid superconductor critical current density (A/m2) at beginning-of-pulse

j_cs_conductor_critical_flat_top_end = 0.0 class-attribute instance-attribute

central solenoid superconductor critical current density (A/m2) at end-of-flattop

jcableoh_bop = 0.0 class-attribute instance-attribute

central solenoid cable critical current density (A/m2) at beginning-of-pulse

jcableoh_eof = 0.0 class-attribute instance-attribute

central solenoid cable critical current density (A/m2) at end-of-flattop

n_pf_cs_plasma_circuits = 0 class-attribute instance-attribute

number of PF circuits (including central solenoid and plasma)

n_pf_coils_in_group = field(default_factory=(lambda: np.array([1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]))) class-attribute instance-attribute

number of PF coils in group j

n_cs_current_filaments = 7 class-attribute instance-attribute

number of filaments the top and bottom of the central solenoid should be broken into during scaling (5 - 10 is good)

n_pf_coil_groups = 3 class-attribute instance-attribute

number of groups of PF coils. Symmetric coil pairs should all be in the same group

n_cs_pf_coils = 0 class-attribute instance-attribute

number of PF coils (excluding the central solenoid) + 1

f_z_cs_tf_internal = 0.71 class-attribute instance-attribute

Central solenoid height / TF coil internal height

f_a_cs_turn_steel = 0.5 class-attribute instance-attribute

Fraction of CS turn poloidal area that is steel (iteration variable 122)

pf_current_safety_factor = 1.0 class-attribute instance-attribute

Ratio of permissible PF coil conductor current density to critical conductor current density based on short-sample DC measurements

pfcaseth = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

steel case thickness for PF coil i (m)

rho_pf_coil = 2.5e-08 class-attribute instance-attribute

PF coil resistivity (if i_pf_conductor=1) (Ohm-m)

rhopfbus = 3.93e-08 class-attribute instance-attribute

Resistivity of CS and PF coil bus bars (irrespective of whether the coils themselves are superconducting or resistive) (Ohm-m)

m_pf_coil_max = 0.0 class-attribute instance-attribute

mass of heaviest PF coil (tonnes)

r_pf_coil_outer_max = 0.0 class-attribute instance-attribute

radius of largest PF coil (m)

p_pf_electric_supplies_mw = 0.0 class-attribute instance-attribute

Total mean wall plug power dissipated in PFC and CS power supplies (MW) (issue #713)

p_cs_resistive_flat_top = 0.0 class-attribute instance-attribute

central solenoid resistive power during flattop (W)

p_pf_coil_resistive_total_flat_top = 0.0 class-attribute instance-attribute

total PF coil resistive losses during flattop (W)

r_pf_coil_inner = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

inner radius of coil i (m)

r_pf_coil_outer = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

outer radius of coil i (m)

c_pf_cs_coils_peak_ma = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

peak current in coil i (MA-turns)

j_pf_coil_wp_peak = field(default_factory=(lambda: np.full(NGC2, 30000000.0))) class-attribute instance-attribute

average winding pack current density of PF coil i (A/m2) at time of peak current in that coil (calculated for i_pf_location=1 coils)

j_cs_critical_flat_top_end = 0.0 class-attribute instance-attribute

allowable central solenoid current density at end of flat-top (A/m2)

j_cs_critical_pulse_start = 0.0 class-attribute instance-attribute

allowable central solenoid current density at beginning of pulse (A/m2)

j_pf_wp_critical = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

allowable winding pack current density of PF coil i (A/m2)

r_cs_middle = 0.0 class-attribute instance-attribute

radius to the centre of the central solenoid (m)

dz_cs_full = 0.0 class-attribute instance-attribute

Full height of the central solenoid (m)

dr_pf_tf_outboard_out_offset = 1.5 class-attribute instance-attribute

radial distance (m) from outboard TF coil leg to centre of i_pf_location=3 PF coils

r_pf_coil_middle = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

radius of PF coil i (m)

dr_pf_cs_middle_offset = 0.0 class-attribute instance-attribute

offset (m) of radial position of i_pf_location=1 PF coils from being directly above the central solenoid

rpf2 = -1.63 class-attribute instance-attribute

offset (m) of radial position of i_pf_location=2 PF coils from being at rmajor (offset = rpf2*triang*rminor)

rref = field(default_factory=(lambda: np.full(N_PF_GROUPS_MAX, 7.0))) class-attribute instance-attribute

PF coil radial positioning adjuster: - for groups j with i_pf_location(j) = 1; rref(j) is ignored - for groups j with i_pf_location(j) = 2; rref(j) is ignored - for groups j with i_pf_location(j) = 3; rref(j) is ignored - for groups j with i_pf_location(j) = 4; rref(j) is radius of the coil in units of minor radii from the major radius (r = rmajor + rref*rminor)

s_shear_cs_peak = 0.0 class-attribute instance-attribute

Maximum shear stress (Tresca criterion) coils/central solenoid [MPa]

sigpfcalw = 500.0 class-attribute instance-attribute

maximum permissible tensile stress (MPa) in steel coil cases for superconducting PF coils (i_pf_conductor=0)

sigpfcf = 1.0 class-attribute instance-attribute

fraction of JxB hoop force supported by steel case for superconducting PF coils (i_pf_conductor=0)

ind_pf_cs_plasma_mutual = field(default_factory=(lambda: np.zeros((NGC2, NGC2)))) class-attribute instance-attribute

mutual inductance matrix (H)

temp_cs_superconductor_margin = 0.0 class-attribute instance-attribute

Central solenoid temperature margin (K)

n_pf_coil_turns = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

number of turns in PF coil i

f_a_pf_coil_void = field(default_factory=(lambda: np.full(NGC2, 0.3))) class-attribute instance-attribute

winding pack void fraction of PF coil i for coolant

f_a_cs_void = 0.3 class-attribute instance-attribute

void fraction of central solenoid conductor for coolant

vs_cs_pf_total_burn = 0.0 class-attribute instance-attribute

total flux swing available for burn (Wb)

vs_pf_coils_total_burn = 0.0 class-attribute instance-attribute

flux swing from PF coils for burn (Wb)

vs_pf_coils_total_ramp = 0.0 class-attribute instance-attribute

flux swing from PF coils for startup (Wb)

vs_pf_coils_total_pulse = 0.0 class-attribute instance-attribute

total flux swing from PF coils (Wb)

vs_cs_total_pulse = 0.0 class-attribute instance-attribute

total flux swing from the central solenoid (Wb)

vs_cs_burn = 0.0 class-attribute instance-attribute

central solenoid flux swing for burn (Wb)

vs_cs_ramp = 0.0 class-attribute instance-attribute

central solenoid flux swing for startup (Wb)

vs_cs_pf_total_ramp = 0.0 class-attribute instance-attribute

total flux swing for startup (constraint eqn 51 to enforce vs_cs_pf_total_ramp=vs_plasma_res_ramp+vs_plasma_ind_ramp) (Wb)

vs_cs_pf_total_pulse = 0.0 class-attribute instance-attribute

total flux swing for pulse (Wb)

f_c_pf_cs_peak_time_array = field(default_factory=(lambda: np.zeros((NGC2, 6)))) class-attribute instance-attribute

PF, CS coil current relative to peak current at time points 1 to 6

m_pf_coil_conductor_total = 0.0 class-attribute instance-attribute

total mass of the PF coil conductor (kg)

m_pf_coil_structure_total = 0.0 class-attribute instance-attribute

total mass of the PF coil structure (kg)

m_pf_coil_conductor = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

conductor mass for PF coil i (kg)

m_pf_coil_structure = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

structure mass for PF coil i (kg)

z_pf_coil_upper = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

upper point of PF coil i (m)

z_pf_coil_lower = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

lower point of PF coil i (m)

z_pf_coil_middle = field(default_factory=(lambda: np.zeros(NGC2))) class-attribute instance-attribute

z (height) location of PF coil i (m)

zref = field(default_factory=(lambda: np.array([3.6, 1.2, 2.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]))) class-attribute instance-attribute

PF coil vertical positioning adjuster: - for groups j with i_pf_location(j) = 1; zref(j) is ignored - for groups j with i_pf_location(j) = 2 AND itart=1 (only); zref(j) is distance of centre of PF coil from inside edge of TF coil (remember that PF coils for STs lie within the TF coil) - for groups j with i_pf_location(j) = 3; zref(j) = ratio of height of coil group j to plasma minor radius - for groups j with i_pf_location(j) = 4; zref(j) = ratio of height of coil group j to plasma minor radius

b_cs_limit_max = 13.0 class-attribute instance-attribute

Central solenoid max field limit [T]

f_dr_dz_cs_turn = 70.0 / 22.0 class-attribute instance-attribute

Ratio of CS coil turn conduit length to depth

dr_cs_turn = 0.0 class-attribute instance-attribute

Length of CS of CS coil turn conduit

dr_cs_full = 0.0 class-attribute instance-attribute

Full radial thickness of the central solenoid (m)

dz_cs_turn = 0.0 class-attribute instance-attribute

Depth/width of CS of CS coil turn conduit

radius_cs_turn_corners = 0.003 class-attribute instance-attribute

Radius of curvature of CS coil turn corners (m)

radius_cs_turn_cable_space = 0.0 class-attribute instance-attribute

Length of CS of CS coil turn conduit length